# What is really the Scale or Sigma parameter of a tobit regression?

In this most upvoted CV answer on that topic the "scale" parameter (aka "sigma" in Stata) thrown in a tobit regression output is explained to be "the estimated standard deviation of the residuals". (Since the question is over three years old, I decided to open a new one.) "That value can be compared to the standard deviation of [the dependent variable]. If it is much smaller, [we] may have a reasonably good model."

However, when I look at the standard deviation of the residuals the values won't match up. Actually "scale" is more than twice the sd of the residuals!

### Example

library(AER)
data(Affairs)
fit <- tobit(affairs ~ age + yearsmarried + religiousness +
occupation + rating, data=Affairs)

fit$scale # the "scale" value # [1] 8.24708 sd(resid(fit)) # sd of residuals # [1] 4.140131 sd(Affairs$affairs)  # sd of dependent variable
# [1] 3.298758


Do I misinterpret that answer, or is it flawed? Could someone clear up with this confusion about the "Scale" (Stata: "Sigma") parameter of a tobit regression? How is it calculated, and what does it tell us about the model quality?